= Toric blowup along an orbit closure
{title2=$v_{\mathrm{new}}=v_1+\cdots+v_k$}
On a smooth <toric variety>, the <blowup> along the <orbit closure in a toric variety> of a cone generated by part of a <lattice basis> $v_1,\ldots,v_k$ is the <star subdivision> at their sum. Locally the center has ideal $(x_1,\ldots,x_k)$; its blowup charts adjoin $x_j/x_i$, producing precisely these subdivided cones. This extends the <toric blowup at a torus-fixed point> to invariant centers of any codimension.
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